A Node-Dependent Kinematic Approach for Rotordynamics Problems

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Matteo Filippi ◽  
Enrico Zappino ◽  
Erasmo Carrera
Keyword(s):  
Dynamic Analysis ◽  
Computational Cost ◽  
Three Dimensional ◽  
Governing Equations ◽  
Three Dimensional Model ◽  
Flexible Supports ◽  
Out Of Plane ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Kinematic Approach

This paper presents the dynamic analysis of rotating structures using node-dependent kinematics (NDK) one-dimensional (1D) elements. These elements have the capabilities to assume a different kinematic at each node of a beam element, that is, the kinematic assumptions can be continuously varied along the beam axis. Node-dependent kinematic 1D elements have been extended to the dynamic analysis of rotors where the response of the slender shaft, as well as the responses of disks, has to be evaluated. Node dependent kinematic capabilities have been exploited to impose simple kinematic assumptions along the shaft and refined kinematic models where the in- and out-of-plane deformations appear, that is, on the disks. The governing equations of the rotordynamics problem have been derived in a unified and compact form using the Carrera unified formulation. Refined beam models based on Taylor and Lagrange expansions (LEs) have been considered. Single- and multiple-disk rotors have been investigated. The effects of flexible supports have also been included. The results show that the use of the node-dependent kinematic elements allows the accuracy of the model to be increased only where it is required. This approach leads to a reduction of the computational cost compared to a three-dimensional model while the accuracy of the results is preserved.

Analysis of Complex Structures Coupling Variable Kinematics One-Dimensional Models

2014 ◽  
Author(s):  
Erasmo Carrera ◽  
Enrico Zappino
Keyword(s):  
Mechanical Design ◽  
Computational Cost ◽  
Advanced Materials ◽  
Complex Structures ◽  
Displacement Fields ◽  
One Dimensional ◽  
Classical Models ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Dimensional Models

One-dimensional models are widely used in mechanical design. Classical models, Euler-Bernoulli or Timoshenko, ensure a low computational cost but are limited by their assumptions, many refined models were proposed to overcome these limitations and extend one-dimensional models at the analysis of complex geometries or advanced materials. In this work a new approach is proposed to couple different kinematic models. A new finite element is introduced in order to connect one-dimensional elements with different displacement fields. The model is derived in the frameworks of the Carrera Unified Formulation (CUF), therefore the formulation can be written in terms of fundamental nuclei. The results show that the use variable kinematic models allows the computational costs to be reduced without reduce the accuracy, moreover, refined-one dimensional models can be used in the analysis of complex structures.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1997 ◽  
Author(s):  
Kevin I. Tzou ◽  
Jonathan A. Wickert ◽  
Adnan Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

Abstract The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

scholarly journals A flash-based thermal simulation of scanning paths in LPBF additive manufacturing

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Kamel Ettaieb ◽  
Sylvain Lavernhe ◽  
Christophe Tournier
Keyword(s):  
High Performance ◽  
Laser Scanning ◽  
Thermal Field ◽  
Computational Cost ◽  
Three Dimensional ◽  
Three Dimensional Model ◽  
Content Type ◽  
Proposed Model ◽  
Scanning Path

Purpose This paper aims to propose an analytical thermal three-dimensional model that allows an efficient evaluation of the thermal effect of the laser-scanning path. During manufacturing by laser powder bed fusion (LPBF), the laser-scanning path influences the thermo-mechanical behavior of parts. Therefore, it is necessary to validate the path generation considering the thermal behavior induced by this process to improve the quality of parts. Design/methodology/approach The proposed model, based on the effect of successive thermal flashes along the scanning path, is calibrated and validated by comparison with thermal results obtained by FEM software and experimental measurements. A numerical investigation is performed to compare different scanning path strategies on the Ti6Al4V material with different stimulation parameters. Findings The simulation results confirm the effectiveness of the approach to simulate the thermal field to validate the scanning strategy. It suggests a change in the scale of simulation thanks to high-performance computing resources. Originality/value The flash-based approach is designed to ensure the quality of the simulated thermal field while minimizing the computational cost.

Evaluation of In-Plane and Out-of-Plane Stresses in Composite Structures Subjected to Large Displacements/Rotations

2018 ◽  
Author(s):  
Alfonso Pagani ◽  
Riccardo Augello ◽  
Erasmo Carrera
Keyword(s):  
Stress Tensor ◽  
Composite Structures ◽  
Structural Model ◽  
Three Dimensional ◽  
Large Displacements ◽  
Nonlinear Stress ◽  
Out Of Plane ◽  
Post Buckling ◽  
Carrera Unified Formulation ◽  
Laminated Structures

In many engineering applications, such as civil, mechanical and aerospace, large displacements and rotations may occur within the working composite structures, due to the extreme loading conditions that may occur during service. This afflicts the equilibrium states of the structures and could change them, eventually, in a catastrophic manner. Therefore, it may be necessary to predict the nonlinear stress conditions of the laminated structures through numerical simulation, in order to prevent the failure of the entire system. To take into account these conditions, a geometrical nonlinear analysis has to be performed. The nonlinear framework proposed in this work is based on the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation that considers the order of the structural model as an input of the analysis, so that no specific formulations are needed to obtain any refined model. The possibility to generate high-order structural elements makes possible to analyze any loading cases, including the post-buckling situation. Furthermore, this methodology allows to evaulate of the full three-dimensional stress tensor in laminated structures. In fact, as CUF is able to calculate the stiffness matrix in an automatic manner, there is no need to include any simplification to evaluate the out-of-plane components of the stress tensor.

In-Plane Vibration Modes of Arbitrarily Thick Disks

1998 ◽  
Vol 120 (2) ◽  
pp. 384-391 ◽  
Author(s):  
K. I. Tzou ◽  
J. A. Wickert ◽  
A. Akay
Keyword(s):  
Natural Frequencies ◽  
Arbitrary Dimension ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Three Dimensional Model ◽  
Bending Vibration ◽  
Annular Disk ◽  
Out Of Plane ◽  
Plane Bending

The three-dimensional vibration of an arbitrarily thick annular disk is investigated for two classes of boundary conditions: all surfaces traction-free, and all free except for the clamped inner radius. These two models represent limiting cases of such common engineering components as automotive and aircraft disk brakes, for which existing models focus on out-of-plane bending vibration. For a disk of significant thickness, vibration modes in which motion occurs within the disk’s equilibrium plane can play a substantial role in-setting its dynamic response. Laboratory experiments demonstrate that in-plane modes exist at frequencies comparable to those of out-of-plane bending even for thickness-to-diameter ratios as small as 10−1. The equations for three-dimensional motion are discretized through the Ritz technique, yielding natural frequencies and mode shapes for coupled axial, radial, and circumferential deformations. This treatment is applicable to “disks” of arbitrary dimension, and encompasses classical models for plates, bars, cylinders, rings, and shells. The solutions so obtained converge in the limiting cases to the values expected from the classical theories, and to ones that account for shear deformation and rotary inertia. The three-dimensional model demonstrates that for geometries within the technologically-important range, the natural frequencies of certain in- and out-of-plane modes can be close to one another, or even identically repeated.

Computationally Efficient Thermo-Mechanical Analysis for Predicting Process-Induced Deformations of Composite Structures

2019 ◽  
Author(s):  
Enrico Zappino ◽  
Navid Zobeiry ◽  
Marco Petrolo ◽  
Reza Vaziri ◽  
Erasmo Carrera ◽  
...  
Keyword(s):  
Composite Structures ◽  
Three Dimensional ◽  
Mechanical Analysis ◽  
Complex Stress ◽  
Curing Process ◽  
Computationally Efficient ◽  
Dimensional Solution ◽  
Kinematic Models ◽  
Carrera Unified Formulation ◽  
Complex Stress Field

Abstract This paper presents an innovative numerical model for the calculation of process-induced deformations of composite structures. The capabilities of a refined one-dimensional model, based on the Carrera Unified Formulation, have been exploited to describe the complex displacement field that originates during the curing process of a composite component. The refined kinematic models adopted are able to describe a three-dimensional solution and make it possible to predict the through-thickness deformation that is one of the causes of the origins of the process-induced deformations. The evolution of the material properties during the curing process is evaluated using the software RAVEN and the manufacturing process is simulated using an ‘incrementally elastic’ constitutive model. The results demonstrate the capabilities of the present approach to predict the process-induced deformations including the complex stress field due to thermal and mechanical loads.

Dynamic Analysis of Rigid-Body Mechanisms Mounted on Flexible Support Structures — Planar Case

2006 ◽  
Vol 505-507 ◽  
pp. 589-594 ◽  
Author(s):  
Huai Ku Sun ◽  
Cun Gin Chen ◽  
Yu Chen Shen
Keyword(s):  
Rigid Body ◽  
Dynamic Analysis ◽  
Flexible Structures ◽  
Three Dimensional ◽  
Support Structures ◽  
Three Dimensional Model ◽  
Element Analysis ◽  
Planar Case ◽  
Flexible Support ◽  
Future Work

Computer-aided analysis of rigid-body mechanisms is combined with the finite element analysis of flexible structures to develop a computer model and derive the equation of motion, incorporating the Lagrange multiplier, to be used in the dynamic analysis of multi-rigid-body mechanisms mounted on flexible support structures. The resulting equations are solved by numerical integration. Predicting and analyzing the performance of the full system, including the motion of the system components and the forcing condition, during the engineering design process will promote the success of the entire system. Finally, a machine gun system with a flexible mount is given as a numerical example. The results reveal that the interaction between the rigid-body mechanisms and its flexible support structures importantly determines the performance of whole system. This study considers only the planar case. Our future work will propose a more complicated fully three-dimensional model.

Dynamical Simulation about Buffer Packaging of Computer

2011 ◽  
Vol 55-57 ◽  
pp. 1711-1724
Author(s):  
Guo Qing Zhang ◽  
Jing Huang ◽  
Hai Bo Lin
Keyword(s):  
Dynamic Analysis ◽  
Modal Analysis ◽  
Three Dimensional ◽  
Fixed Frequency ◽  
Three Dimensional Model ◽  
Sinusoidal Vibration ◽  
Transient Dynamic Analysis ◽  
Transient Dynamic ◽  
Inherent Frequency ◽  
Thin Steel Plate

A host computer packaging cushion is designed, including deflection, buffering capacity, creep checking. Then g a three-dimensional model of the host buffer packaging systems is established Simulation of the system, including static analysis, modal analysis, harmonic analysis and transient dynamic analysis. Finally, the physical system is used to do the sine frequency, fixed-frequency sinusoidal vibration test. the vulnerability of the buffer package sinusoidal frequency calculate by the computer modal analysis larger than the resonance frequency of the measured test values This is due to host the actual shell of the computer by each side made of thin steel plate riveting, and list them in the computer simulation as a whole in the shell, so that the overall stiffness of the system become larger, so that the analysis of the inherent frequency than the actual value. Transient dynamic analysis of the computer meets the fixed-frequency sinusoidal test results，which are all happened in the prophase of vibration in the balance position. This vibration last a period causing fatigue, so that the acceleration package increases slowly and the product damage.

Stress analysis in transverse loading of soft core sandwich plates with various boundary conditions

2018 ◽  
Vol 22 (8) ◽  
pp. 2692-2734 ◽  
Author(s):  
Isa Ahmadi
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Stress Singularity ◽  
Sandwich Plates ◽  
Local Concentration ◽  
Governing Equations ◽  
Transverse Loading ◽  
Weak Formulation ◽  
Various Boundary Conditions ◽  
Out Of Plane

In this paper, the transverse loading of sandwich plate is formulated to study the three-dimensional stress field in the sandwich plates for various edge conditions. The formulation is based on the weak formulation approach. A complete three-dimensional displacement field is considered and the weak formulation approach is employed to obtain the governing equations of the plate using the three dimensional equilibrium equations of elasticity. An analytical solution is presented for governing equations when two opposite edges of plate are simply supported. A one-step stress recovery scheme is used to compute the out-of-plane stresses in the sandwich plates. A comparison is made with the predictions of exact elasticity solutions in the open literature and very good agreements are achieved. The distribution of stresses is investigated for various boundary conditions and the log-linear procedure is employed to study the order of stress singularity at free and clamped edge of the plate. It is seen that the present approach accurately predicts the distribution of out-of-plane stresses and local concentration of stresses in the vicinity of free and clamped edges of sandwich structures.

Research on the Dynamic Characteristics of Strain Tower in Heavy Icing Area Based on SAP2000

2014 ◽  
Vol 986-987 ◽  
pp. 681-684
Author(s):  
Shi Long Wang ◽  
Qi Xiang Lin ◽  
Ying Qian
Keyword(s):  
Dynamic Analysis ◽  
Response Spectrum ◽  
Economic Value ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Analysis Software ◽  
Three Dimensional Model ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Set Up

This paper is a further analysis of the strain tower on 1YD - JC4.After making a static analysis of 1YD - JC4 strain tower,we select the best offset point and make a dynamic analysis of it.Based on the finite element analysis software SAP2000, we set up a three-dimensional model of 1YD - JC4 strain tower of 110kv about heavy icing area,and then obtain the first six modal frequencies after making a dynamic analysis . We then draw the response spectrum curve.in the end, we select the safe and economic value of damping according to the curve.

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